Grain boundary structural transformation induced by co-segregation of aliovalent dopants

Impurity doping is a conventional but one of the most effective ways to control the functional properties of materials. In insulating materials, the dopant solubility limit is considerably low in general, and the dopants often segregate to grain boundaries (GBs) in polycrystals, which significantly alter their entire properties. However, detailed mechanisms on how dopant atoms form structures at GBs and change their properties remain a matter of conjecture. Here, we show GB structural transformation in α-Al2O3 induced by co-segregation of Ca and Si aliovalent dopants using atomic-resolution scanning transmission electron microscopy combined with density functional theory calculations. To accommodate large-sized Ca ions at the GB core, the pristine GB atomic structure is transformed into a new GB structure with larger free volumes. Moreover, the Si and Ca dopants form a chemically ordered structure, and the charge compensation is achieved within the narrow GB core region rather than forming broader space charge layers. Our findings give an insight into GB engineering by utilizing aliovalent co-segregation.

core, we could not find Si L-edges at the GB core. This is because the strong Al-L2,3 and the related minor edges are completely overlapped with the Si-L2,3 edge. Therefore, it is difficult to experimentally confirm the electronic structure of Si at the GB core. It is noteworthy that all the peaks of Al at the GB core become broader than that in the bulk, which is the most evident in the onset of Al-L3 edge, as indicated by the arrows in Suppl. Fig. 5b. The downward energy shift is 1.2 eV, corresponding to the lower coordination number at the GB core [2].
Supplementary Figure 6c shows the Ca-L2,3 edge at the GB core, and the profile is similar to that of CaO [3], suggesting that the oxidation state of Ca should be 2+ (Ca !" #$ ) at the GB core.

Supplementary Note 3.
To evaluate the Ca occupation at the site A ( Fig. 2), we performed multi-slice image simulations using the frozen phonon model with a 200 kV electron probe, illumination semi-angle of 24 mrad, and an ADF detector spanning 64 to 150 mrad [4]. The frozen phonon calculation assumed an Einstein model and used 10 phonon configurations. On the basis of the log-ratio method in EELS, the specimen thickness was estimated to be 15 ± 3 nm, and we assumed the specimen thickness as 14.2 nm in our image simulation, which contains 30 atoms in the Ca atomic column. There are too many configurations along the projection when considering the multiple Al sites at the A site. Therefore, we used the fractional atomic potential for Ca rather than considering the configuration of Ca !" #$ . Suppl. Fig. 7a shows the experimental and simulated ADF-STEM images with the Ca occupation between 50% and 100%, and the Z-contrast intensity at the Ca atomic column increases as a function of Ca occupation. Suppl. Fig. 7b shows the experimental and simulated Z-contrast intensity profiles along the A-B direction, where the intensities are normalized to the Al atomic column as indicated by the red arrowhead. The error bars in the experimental profile corresponds to standard deviation, which were calculated from the 5 different line profiles. Comparing the experiment with simulations, the Ca occupation may be estimated to be 90 ± 10%, suggesting that the Ca atomic column could be almost fully occupied. We note that the present comparison was performed in the relative intensity rather than the absolute-intensity scale, and therefore the reliability of this quantification may be limited.

Supplementary Note 4.
To investigate the possible formation of the charged GB and the spacecharge layer, we performed macroscopic electrostatic calculations using the standard Gouy-Chapman model. As an example, we considered the positively charged M(Al) 1×1 GB with one Ca !" #$ and two Si !" #% in the GB structure unit. In this case, we assumed that Ca !" #$ would distribute around the positively charged GB core (originate from the extra Si !" #% ) to form the space-charge layer. We evaluated the electrostatic potential and the Ca !" #$ concentration profiles in the space-charge layer as follows. When the positively charged GB is formed, the electrostatic potential around the GB should be higher than that in the bulk, and we denote this extra electrostatic potential as ϕ(x) (x: distance from the GB core). Using the Boltzmann distribution with the defect formation energy of Ca !" #$ in the bulk, the Ca !" #$ concentration profile c(x, T) can be written as where cb(T) is the solubility limit of Ca !" #$ in the bulk at an absolute temperature T, and k is the Boltzmann constant. The electrostatic potential ϕ(x) in the space-charge layer can be evaluated by solving the Poisson's equation with the boundary condition: . ! ((*) . . .((*) where ϵ is the permittivity of α-Al2O3. These equations of (1) -(3) can be transformed into the following differential equation: . The electrostatic potential around the GB ϕ(x) is determined self-consistently to satisfy the following charge-neutrality between the GB core and the space-charge layer: where qGB is the charge density at the GB. By numerically solving the differential equation (4), we evaluated the electrostatic potential ( ) and the Ca !" #$ concentration ( , ). Suppl. Figs.
8a and 8b show the electrostatic potential and the Ca !" #$ concentration at the sintering temperature of 1773 K, respectively. Although the electrostatic potential spans several μm from the GB, the Ca !" #$ is localized within only a few Å from the GB core, i.e., 98.4 % of the Ca !" #$ is localized within 5 Å from GB core. This result strongly suggests that the formation of charged GB and the space-charge layer is unfavorable, but the charge compensation would be achieved locally within the GB core.